Equivalence between supersymmetric self-dual and Maxwell-Chern-Simons models coupled to a matter spinor superfield

We study the duality of the supersymmetric self-dual and Maxwell-Chern-Simons theories coupled to a fermionic matter superfield, using a master action. This approach evades the difficulties inherent to the quartic couplings that appear when matter is represented by a scalar superfield. The price is that the spinorial matter superfield represents a unusual supersymmetric multiplet, whose main physical properties we also discuss. (C) 2009 Elsevier B.V. All rights reserved.

On duality of the noncommutative supersymmetric Maxwell-Chern-Simons theory

We study the possibility of establishing the dual equivalence between the noncommutative supersymmetric Maxwell-Chern-Simons theory and the noncommutative supersymmetric self-dual theory. It turns to be that whereas in the commutative case the Maxwell-Chern-Simons theory can be mapped into the sum of the self-dual theory and the Chern-Simons theory, in the noncommutative case such a mapping is possible only for the theory with modified Maxwell term. (c) 2008 Elsevier B.V. All rights reserved.

Remarks on charged vortices in the Maxwell-Chern-Simons model

We study vortex-like configuration in Maxwell-Chern-Simons electrodynamics. Attention is paid to the similarity it shares with the Nielsen-Olesen solutions at large distances. A magnetic symmetry between a point-like and an azimuthal-like current in this framework is also pointed out. Furthermore, we address the issue of a neutral spinless particle interacting with a charged vortex, and obtain that the Aharonov-Casher-type phase depends upon mass and distance parameters. (C) 2003 Published by Elsevier B.V.

Quantum equivalence between the self-dual and the Maxwell-Chern-Simons models nonlinearly coupled to U(1) scalar fields

The use of master actions to prove duality at quantum level becomes cumbersome if one of the dual fields interacts nonlinearly with other fields. This is the case of the theory considered here consisting of U(1) scalar fields coupled to a self-dual field through a linear and a quadratic term in the self-dual field. Integrating perturbatively over the scalar fields and deriving effective actions for the self-dual and the gauge field we are able to consistently neglect awkward extra terms generated via master action and establish quantum duality up to cubic terms in the coupling constant. The duality holds for the partition function and some correlation functions. The absence of ghosts imposes restrictions on the coupling with the scalar fields.

Soluções do tipo vórtice em um modelo de Maxwell-Chern-Simons-Higgs com campos de Gauge distintos

Pós-graduação em Física - FEG

Vortices in (Abelian) Chern-Simons gauge theory

The vortex solutions of various classical planar field theories with (Abelian) Chern-Simons term are reviewed. Relativistic vortices, put forward by Paul and Khare, arise when the Abelian Higgs model is augmented with the Chern-Simons term. Adding a suitable sixth-order potential and turning off the Maxwell term provides us with pure Chern-Simons theory, with both topological and non-topological self-dual vortices, as found by Hong-Kim-Pac, and by Jackiw-Lee-Weinberg. The non-relativistic limit of the latter leads to non-topological Jackiw-Pi vortices with a pure fourth-order potential. Explicit solutions are found by solving the Liouville equation. The scalar matter field can be replaced by spinors, leading to fermionic vortices. Alternatively, topological vortices in external field are constructed in the phenomenological model proposed by Zhang-Hansson-Kivelson. Non-relativistic Maxwell-Chern-Simons vortices are also studied. The Schrodinger symmetry of Jackiw-Pi vortices, as well as the construction of some time-dependent vortices, can be explained by the conformal properties of non-relativistic space-time, derived in a Kaluza-Klein-type framework. (c) 2009 Elsevier B.V. All rights reserved.

Efeito Casimir em teorias de Chern-Simons

Nesta dissertação obtemos a força de Casimir a temperatura finita entre duas linhas paralelas sujeitas a condição de fronteira do tipo linhas mistas, no contexto da teoria de Maxwell- Chern-Simons em (2+1) dimensões. Além disso, analisamos a simetria de inversão de temperatura apresentada pela energia livre de Helmholtz do modelo para diferentes condições de fronteira. Iniciamos estudando aspectos gerais do formalismo de Matsubara no intuito de introduzirmos efeitos térmicos na teoria; também analisamos aspectos gerais da teoria de MCS em (2 + 1) dimensões. Posteriormente, revisitamos o cálculo da força de Casimir para o caso de duas linhas paralelas infinitamente permeáveis magneticamente a temperatura nula e finita, bem como o caso de linhas mistas a temperatura nula, onde tomamos uma linha perfeitamente condutora eletricamente e outra infinitamente permeável magneticamente. Em seguida, apresentamos novos resultados envolvendo a força de Casimir a temperatura finita com condições de fronteira do tipo linhas mistas. Por último, analisamos a simetria de inversão de temperatura associada a energia livre de Helmholtz do modelo, mostrando que mesmo para condições mistas e possível obter uma espécie de simetria residual, em analogia a resultados existentes para a eletrodinâmica em (3+1) dimensões.

Soluções tipo vórtex em teorias de gauge Chern-Simons-Maxwell-Higgs

Pós-graduação em Física - IFT

Chern-Simons vortices and holography

In this paper, based on the AdS(4)/CFT3 duality, we have explored the precise connection between the abelian Chern-Simons (CS) Higgs model in (2 + 1) dimensions to that with its dual gravitational counterpart living in one higher dimension. It has been observed that theU(1) current computed at the boundary of the AdS(4) could be expressed as the local function of the vortex solution that has the remarkable structural similarity to that with the Ginzburg-Landau (GL) type local expression for the current associated with the Maxwell-CS type vortices in (2 + 1) dimensions. In order to explore this duality a bit further we have also computed the coherence length as well as the magnetic penetration depth associated with these vortices. Finally using the knowledge of both the coherence length as well as the magnetic penetration depth we have computed the Ginzburg-Landau coefficient for the Maxwell-CS type vortices in (2 + 1) dimensions.

Higher derivative Chern-Simons extension in the noncommutative QED(3)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Four-dimensional current algebra from Chern-Simons theory

We study an abelian Chern-Simons theory on a five-dimensional manifold with boundary. We find it to be equivalent to a higher-derivative generalization of the abelian Wess-Zumino-Witten model on the boundary. It contains a U(1) current algebra with an operational extension.

Supersymmetric Chern-Simons theories with vector matter

In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic vector matter. In particular we present an exact calculation of the free energy of the N = 2 supersymmetric model (with one chiral field) for all values of the `t Hooft coupling in the large N limit. This is done by using a generalization of the standard Hubbard-Stratanovich method because the SUSY model contains higher order polynomial interactions.

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N vertical bar N = 1). The algebra for the N = 3 case is written down explicitly using the fact that it arises as the global part of the super conformal W-3 superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N - 1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N >= 4, the sl(N|N - 1) theory admits smooth supersymmetric conical defects.

3D gravity, Chern-Simons and higher spins: A mini introduction

We give a review on (a) elements of (2 + 1)-dimensional gravity, (b) some aspects of its relation to Chern-Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an application in the context of flat space higher spin theory. A knowledge of the Einstein-Hilbert action, classical non-Abelian gauge theory and some (negotiable amount of) maturity are the only pre-requisites.

Three-dimensional superconformal field theory, Chern-Simons theory, and their correspondence

In this thesis, we discuss 3d-3d correspondence between Chern-Simons theory and three-dimensional N = 2 superconformal field theory. In the 3d-3d correspondence proposed by Dimofte-Gaiotto-Gukov information of abelian flat connection in Chern-Simons theory was not captured. However, considering M-theory configuration giving the 3d-3d correspondence and also other several developments, the abelian flat connection should be taken into account in 3d-3d correspondence. With help of the homological knot invariants, we construct 3d N = 2 theories on knot complement in 3-sphere for several simple knots. Previous theories obtained by Dimofte-Gaiotto-Gukov can be obtained by Higgsing of the full theories. We also discuss the importance of all flat connections in the 3d-3d correspondence by considering boundary conditions in 3d N = 2 theories and 3-manifold.